波动方程叠前偏移与波形反演研究

1、波动方程叠前偏移与波形反演研究        【中文摘要】本文就当前反射地震勘探的两个热门题目波动方程叠前深度偏移与基于波动方程的全波形反演进行了多方面的探讨。深度偏移的核心是波场延拓算子的求取,我们编程实现了目前使用较多的几种算子:相移、相移插值、分步傅立叶、傅立叶有限差分以及广义屏算子。数值例子说明,这些算子均有各自的优点和局限,应该根据介质的特点选择成像精度与计算时间可接受的方法。共炮记录的偏移是最直观、易实现、精度高的叠前偏移技术,然而其计算量很大。近些年出现了旨在进步叠前偏移计算效率的多种非共炮记录的偏移

2、方法。其中双平方根偏移基于沉降观测概念,将震源和记录同时向下延拓,计算迅速,而平面波偏移则先对震源和记录做平面波分解,再偏移叠加,是一种有效降低多次覆盖地震记录冗余性的好方法。这两种方法均可为速度分析等输出重要的共成像道集。为给叠前偏移实验提供必要的输进,我们基于惠更斯原理天生了共炮记录,与其它正演方法相比,该方法计算效率高、各种绕射波完整清楚、信噪比高,可以灵活的选择波场延拓算子,并且对观测系统有很好的适应能力,能够方便处理地表起伏时的记录正演题目。起伏地表的处理是困扰复杂地区成像质量的一个关键因素,本文鉴戒Reshef“逐步累加”的波场外推概念,在起伏地表上充填常速度,变不平坦地形为平坦地

3、形,实现了共炮记录的天生和偏移,结果表明,我们的方法是处理复杂地表的简单有效策略。偏移是构造成像的基本手段,然而随着油气勘探的不断深进,人们越来越希看由地震资料获得更多的岩石物性信息,其中高精度的介质速度场亦是偏移成像必要的输进,所以,各种地震反演方法迅速发展起来。由于基于波动方程的波形反演方法直接采用微分方程模型,能够充分利用地震信息,可以得到更加精确可靠的反演结果,近些年景为国内外研究的热门。然而,传统的梯度法反演存在收敛速度慢、不易重建速度场低波数成分的严重缺点,而高斯牛顿法的计算量又很大。我们采用近些年国外学者提出的将虚震源法与互易定理相结合计算雅可比矩阵的方法实现了高斯牛顿法波形反演

4、,并将结果与梯度法做了比较,深进熟悉了波场反演的规律。算例表明,采用这种方法计算雅可比矩阵进行高斯牛顿法反演计算量明显减小,收敛速度快,对速度场的低波数成分重建迅速。我们以为,随着高性能计算机技术的发展,基于波动方程的全波形反演将为更精确的物性成像提供可行的途径。');【Abstract】 We discussed two hot topics in seismic exploration:wave-equation pre-stack migration and waveform inversion. The key point of depth migration is the w

5、ave field extrapolation operator. Several of them have been performed by computer program, they are PS、PSPI、SSF、FFD and GS. Numerical examples indicate that each operator has its advantage and limitation,we must consider imaging accuracy and time consumption according to the feature of the media bef

6、ore migration is performed. The common-shot pre-stack migration is visual、easy to be operated、and high precision, but its calculated amount is huge. In recent years,people have developed several migration techniques which don't use common-shot records in order to improve computational efficiency

7、 for pre-stack migration. Based on survey-sinking concept, double square root equation migration downward continues source and record at the same time,so it is quite efficient. While in plane wave migration,we first perform plane wave decomposition on source and record,then migrate each plane wave d

8、ata. Obviously, the redundancy of multifold seismic record has decreased. Both of the two methods could export common-image gathers for velocity analysis or other use. In order to provide input for pre-stack migration,we generated common-shot record based on Huygens's principle. Compared with ot

9、her modeling strategy,our method is more efficient,the types of wave are more complete and clear,and the signal-to-noise ratio is higher. It enable us to choose wave field extrapolation operator freely. Furthermore,the method is available when the recording geometry is complicated such as rugged ear

10、th su*ce. The processing of relief su*ce is a key factor for imaging in complex area.We follow the concept of Reshef's "step-to-step-accumulation" for wave field extrapolation,filling constant velocity over rugged su*ce,so the su*ce turns into flat one and general way for modeling and

11、migration could be adopted. The computing result shows that it's an effective approach handling complex su*ce. Migration is the basic strategy for structure imaging,however,along with the progress of oil/gas exploration,people eagerly hope to get more information about rock's physical proper

12、ty from seismic data ,meanwhile, velocity field of high accuracy is also necessary as input for migration.Hence,different seismic inversion methods have been developed rapidly. Wave equation waveform inversion adopts differential equation model directly, it could take full advantage of seismic infor

13、mation,get more accurate and reliable inversion result,so it has become hot point.However,traditional gradient method suffers from disadvantage of poor convergence rate and difficulty to reconstruct the low wave number component of the velocity field,while the calculated amount of Gauss-Newton metho

14、d is large .We calculated Jacobian matrix by the way combining virtual source method and reciprocity principle which is proposed by foreign scholars in recent years ,and accomplished Gauss-Newton waveform inversion. We compared it with gradient method,achieving much understanding about the feature of wave field inversion . Numerical example indicates that the calculated amout decreases remarkably when Jacobian matrix is obtained in this way. And the inversion converges fast , the high wave number component of the velocity field is much easier to be recons